Nevertheless, assessing and maximizing the universality of collinear PDFs and FFs is crucial given the increasingly broad scenarios where they are used.
A major focus in the current effort by the Jefferson Lab Angular Momentum (JAM) Collaboration is therefore to both test and broaden the predictive power of parton correlation functions.
This is achieved through a Bayesian inference procedure in which PDFs and FFs are extracted simultaneously, and the uncertainty quantification associated with particular parametrizations of parton correlation functions is given in terms of a Bayesian posterior distribution.
To test universality, the system of equations relating observables to parton correlation functions must of course exceed the total number of correlation functions involved — a minimum requirement is that the parton correlation functions be overconstrained by the data in the fit.
Of course, realizing this in practical analyses requires that all parton correlation functions be truly fitted simultaneously.
This is a major numerical and technological challenge, and traditionally PDFs and FFs have thus been extracted in separate procedures.
However, simultaneous fits can be achieved with the Bayesian Monte Carlo approach, and have been implemented recently in the JAM17 [1]} analysis of helicity PDFs, and in the JAM19 [2]} analysis of unpolarized PDFs and FFs.
The same basic methodology was also applied in the three-dimensional JAM3D20 [3]} study, in the first combined analysis of TMD observables that satisfies the overconstraining criterion.
